True or false questions, indicate a short expansion for each .
(1) if there are no forces acting on a body, the body will experience no acceleration. ( its false on my answer key )
(2) the component of a vector is a vector ( it's true on my answer key )
(3) if a vector is zero, each of its components must be zero . ( it's true on my answer key )
i'm confused

(1).  Your answer key troubles me on this one. 

Newton's second law of motion says:

                        Force = (mass) x (acceleration)

The 'force' in this formula is the 'net' force on an object ...
the combined result of all the forces acting on it.  If the net
force is zero ... either there are a bunch of forces but they
all cancel each other and add up to zero, or there's actually
no force at all acting on the object ... then it's clear from that
simple formula that the acceleration must also be zero.  
My personal opinion is that the statement in (1) is true.

(2).  The components of a big vector are two little vectors that
add up to be equal to the size and direction of the big vector. 
If they didn't both have size and direction of their own, then they
couldn't add up to be a vector.  So each component must be a vector.

(3).  This one is so simple that it's hard to explain.
If you and your big sister are both pulling on a book ... you're pulling
that way /\ and she's pulling that way >, the only way for that book
not to move is for both of you to pull with zero force.  If either of you
pulls with any force, then the book must move.
The components of a vector are perpendicular, like those arrows
that I tried to draw.  The only way the whole vector can be zero is
if both components are zero.

You yeah with the side of the yeah with a little bit of yeah.